Sequence of period doublings and chaotic pulsations in a free boundary problem modeling thermal instabilities

A simplified one-sided model associated with combustion and some phase transitions has been solved numerically. The results show a transition from the basic uniform motion of the free boundary to chaotic pulsations via periodic oscillations and a clearly manifested sequence of period doublings. For both numerical and rigorous treatment, the free boundary problem presents clear advantages over the two commonly used classes of models: the free interface (two-sided) models and the models with distributed kinetics. It is argued that, in view of its generic nature and relative simplicity, the problem may serve as a canonical example of the thermal instability leading to a variety of self-oscillatory regimes.